To free solo is to climb without ropes or support of any kind. It is the purest, and most dangerous, form of climbing. It is you and the rock. To put it more viscerally: If you slip, or miss a handhold, or cramp up and lose your grip, you will fall for a very long time and then you will die.

Here is that same writer's headline about Alex's feat:

Alex Honnold’s free solo climb of El Capitan was dangerous, perhaps insane, and the athletic feat of the century